Related papers: Noncommutative Double Bruhat cells and their facto…
This paper studies the problem of decomposing a low-rank matrix into a factor with binary entries, either from $\{\pm 1\}$ or from $\{0,1\}$, and an unconstrained factor. The research answers fundamental questions about the existence and…
This paper studies the problem of decomposing a low-rank positive-semidefinite matrix into symmetric factors with binary entries, either $\{\pm 1\}$ or $\{0,1\}$. This research answers fundamental questions about the existence and…
We use the framework of matrix factorizations to study topological B-type D-branes on the cubic curve. Specifically, we elucidate how the brane RR charges are encoded in the matrix factors, by analyzing their structure in terms of sections…
We construct six- and four-dimensional toroidal compactifications of the Type I string with magnetic flux on the D-branes. The open strings in this background probe a noncommutative internal geometry. Phenomenologically appealing features…
In this paper we describe new noncommutative factorizations of functions related to $d$-th tensor powers of Carlitz's $\mathbb F_q[\theta]$-module for $d\geq 1$, called higher sine functions. In recent work by the second author,…
We introduce the notion of ungraded matrix factorization as a mirror of non-orientable Lagrangian submanifolds. An ungraded matrix factorization of a polynomial $W$, with coefficients in a field of characteristic 2, is a square matrix $Q$…
Using nonnegative/binary matrix factorization (NBMF), a matrix can be decomposed into a nonnegative matrix and a binary matrix. Our analysis of facial images, based on NBMF and using the Fujitsu Digital Annealer, leads to successful image…
Factorization of the differential expansion coefficients for HOMFLY-PT polynomials of double braids, discovered in arXiv:1606.06015 in the case of rectangular representations $R$, is extended to the first non-rectangular representations…
Matrix factorization techniques have been widely used as a method for collaborative filtering for recommender systems. In recent times, different variants of deep learning algorithms have been explored in this setting to improve the task of…
I review the meaning of ``QCD factorization'' in hadronic two-body B decays and then discuss recent results of theoretical (rather than phenomenological) nature: the proof of factorization at two loops; the identification of ``chirally…
Nonnegative matrix factorization (NMF) is a powerful class of feature extraction techniques that has been successfully applied in many fields, namely in signal and image processing. Current NMF techniques have been limited to a…
We introduce fusion algebras with not necessarily positive structure constants and without identity element. We prove that they are semisimple when tensored with $\mathbb{C}$ and that their characters satisfy orthogonality relations. Then…
We derive the noncommutative torus compactification of M(atrix) theory directly from the string theory by imposing mixed boundary conditions on the membranes. The relation of various dualities in string theory and M(atrix) theory…
Given a nonnegative matrix factorization, $R$, and a factorization rank, $r$, Exact nonnegative matrix factorization (Exact NMF) decomposes $R$ as the product of two nonnegative matrices, $C$ and $S$ with $r$ columns, such as $R = CS^\top$.…
We give the supergravity duals of commutative and noncommutative non-abelian gauge theories with N=2 in 2+1 dimensions. The moduli space on the Coulomb branch of these theories is studied using supergravity.
This is the first one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with almost simple linear groups.
The deterministic recursive pivot-free algorithms for the computation of generalized Bruhat decomposition of the matrix in the field and for the computation of the inverse matrix are presented. This method has the same complexity as…
We use the theory of $\textbf{U}_q$-tilting modules to construct cellular bases for centralizer algebras. Our methods are quite general and work for any quantum group $\textbf{U}_q$ attached to a Cartan matrix and include the non-semisimple…
Double Bruhat cells in a connected complex semisimple Lie group $G$ emerged as a crucial concept in the work of S. Fomin and A. Zelevinsky on total positivity and cluster algebras. These cells are special instances of a broader class of…
In this paper, we study the nonnegative matrix factorization problem under the separability assumption (that is, there exists a cone spanned by a small subset of the columns of the input nonnegative data matrix containing all columns),…